The polynomial function will be x² + (10 - √7)x + 4 ( 6 - √7).
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that the zeroes of the polynomials are 4,6−√7. The polynomial can be written as:-
( x + 4 ) ( x + 6 -√7)
x² + 6x - √7x + 4x 24 - 4√7
x² + ( 10 - √7 )x + 4(6 - √7)
Hence, the polynomial function will be x² + (10 - √7)x + 4 ( 6 - √7).
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The perimeter of a rectangular pool is 368m. If the width of the pool is 86m, what is the length
The length of the rectangular pool is 98 m.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the perimeter of a rectangular pool is 368m.
The width of the pool is 86m
We need to find the length of the pool.
Perimeter of rectangle=2(Length+width)
368=2(Length+86)
368=2Length+172
368-172=2length
196=2length
Divide both sides by 2
98=length
Hence, the length of the rectangular pool is 98 m.
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Lee has made a nonrefundable deposit of the first month’s rent (equal to $900) on a
apartment lease to 6 months. The same day later Lee finds a different apartment that
he likes just as well, but its monthly rent is cheaper and negotiable. Assume a nominal
rate interest rate of 8% convertible monthly. The rent will be paid monthly and at the
beginning of each month.
(i) Write down the cash flow and compute the present value (to 2 decimal numbers)
of 6 months if Lee rents the first apartment ($900).
(ii) Find the range of the rent (to 2 decimal numbers) of the cheaper apartment such
that Lee would switch to rent the new apartment.
Answer:
(i) To calculate the present value of 6 months of rent for the first apartment, we can use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (6 months of rent, or $900 x 6 = $5400), r is the interest rate (8% converted to a monthly rate, or 0.08/12 = 0.0067), and n is the number of periods (6 months). So, PV = $5400 / (1 + 0.0067)^6 = $4911.46
(ii) To find the range of rent for the new apartment such that Lee would switch, we need to find the monthly rent that would result in a present value equal to or greater than $4911.46. Using the same formula, we can solve for the monthly rent (R) by setting PV equal to $4911.46 and n equal to 6. So, $4911.46 = R*(1+0.0067)^6. Solving for R, we get that the monthly rent must be between $732.32 and $766.58 in order to be more favorable than the first apartment.
how many positive integers n satisfy the following condition: (130n)50>n100>2200 ? (a) 0 (b) 7 (c) 12 (d) 65 (e) 125
There are (e) 125 positive integers that satisfy the n condition
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
(130n)^50 > n^100 > 2^200
[tex]\sqrt[50]{}[/tex][(130n)^50] > [tex]\sqrt[50]{}[/tex](n^100) > [tex]\sqrt[50]{}[/tex](2^200)
130n > n^2 > 2^4
130n > n^2 > 16
Solving each part, we get:
n^2 > 16
n > √16
n > 4
130n > n^2
130 > n^2/n
130 > n
130 > n > 4
Therefore the answer is the number of positive integers over 4 and 130 which is 129 - 5 + 1 = 125
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Correctly written question:
How many positive integers n satisfy the following condition (130n)⁵⁰ > n¹⁰⁰ > 2²⁰⁰ ? (a)0 (b)7 (c)12 (d)65 (e)125
Find the tangent of ZZ.
X
39
Z
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan (Z) =
Submit
89
80
Pythagorean theorem
Work it out
Not feeling ready yet? These can help:
Lesson: Trigonometric ratios
The fraction for the value of tan Z is 39/80
What are trigonometric identities?Trigonometric Identities are simply described as equalities that involves several trigonometry functions and also one that holds true for all the values of variables given in the equation.
The types of trigonometric functions as;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Hypotenuse = 89
Opposite side = 39
Adjacent = 80
tan Z = opposite/adjacent
substitute the values
tan Z = 39/80
Hence, the equation is 39/80
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Bonomics and Personal Finance (2020) Sem 2
Points Possible: 30
YOUR ASSIGNMENTS
1. One of the hardest things about handling money is balancing short-term needs and wants with veg
term needs and wants, How can you save money in an interest-bearing account when you need every
penny to pay for school loans, car loans, rent, and utilities? Write one paragraph that explains why
thinking about the future might be important even when you're having a hard time managing the present
A good way to save money in an interest-bearing account is using a savings account with intereste
What is future planning?The future of management relies on flexibility, adaptation and pragmatism.
The following ideas can help you make a plan to save and maximize your interest earnings.
1. High-Yield Savings Account. .
2. High-Yield Checking Account. .
3. CDs and CD Ladders.
4. Money Market Account.
5.. Treasury Bills.
Research suggests that thinking about the future,a process known as prospection,can help us lead more generous and fulfilled lives. Mindfulness is all the rage these days, and for good reason. Focusing on the moment can improve our well-being, foster compassion, and help our relationships.
For a better well-being we have to think about the future.
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C is equidistant to which of the following points
The point C is equidistant to (b) CL = CM = CN
How to determine the equidistant pointsFrom the question, we have the following parameters that can be used in our computation:
The triangle
From the triangle, we can see that the point C is the centroid of the triangle
As a general rule:
The centroid is the geometric centre of a triangle. It is equidistant from all the points present on the triangle.
This means that point C is equidistant from L, M and N
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find the derivative of the function using the definition of the derivative. state the domain of the function and the domain of its derivative. f (t) = 2.5t2 +6 t
Using the definition of the derivative, the derivative of the function is f'(t) = 5t + 6. The domain of the function and its derivative are both the set of all real numbers.
The derivative is a concept in calculus that represents the rate of change or the slope of a function at a specific point. It is defined as the limit of the difference quotient of the function as the interval between the two points approaches zero. Mathematically, the derivative of a function f(x) at a point x is represented as f'(x) and can be expressed as:
f'(x) = lim h -> 0 [f(x + h) - f(x)]/h
where h is the interval between the two points.
The derivative is a fundamental tool for analyzing and understanding the behavior of functions, including their local maxima, minima, and inflection points, as well as for solving problems in physics and engineering.
The derivative of the function f(t) = 2.5t² + 6t can be found using the definition of the derivative:
f'(t) = limit as h -> 0 of [f(t + h) - f(t)]/h
= limit as h -> 0 of [2.5(t + h)² + 6(t + h) - (2.5t² + 6t)]/h
= limit as h -> 0 of [2.5t² + 5ht + 2.5h² + 6t + 6h - 2.5t² - 6t]/h
= limit as h -> 0 of [5ht + 2.5h² + 6h]/h
= limit as h -> 0 of [5t + 2.5h + 6]
= 5t + 6
The domain of the function f(t) = 2.5t^2 + 6t is all real numbers. The domain of its derivative f'(t) = 5t + 6 is also all real numbers.
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Jerry ordered 4 items online. He is charged $2.25 per pound for shipping. The items weighed 3.2 pounds, 3.8 pounds, 4 pounds, and 4.5 pounds. How much will he be charged for shipping? (Round to the nearest cent).
The total amount that he will be charged for the shipping is given as follows:
$34.88.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Jerry is charged $2.25 per pound for shipping, hence the constant is given as follows:
k = 2.25.
Meaning that the equation for the total cost for a weight of x pounds is given as follows:
y = 2.25x.
The total weight is given as follows:
3.2 + 3.8 + 4 + 4.5 = 15.5 pounds.
Hence the total cost is given as follows:
y = 2.25 x 15.5
y = $34.88.
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Explain what are the figure below are functions or not
Given the problem:
Explain what are the figure below functions or not
The left graph is not a function, the right table is a function. To see if a graph is a function, use the vertical line test. Simply draw vertical lines down the graph, or you don't have to if you can imagine it. None of the vertical lines can pass through any points twice. So in this case, look at (6, 4) and (6, 6). Draw a vertical line down at x=6. It fails the vertical line test because the vertical line passes through the two points.
Next, the table on the right. It is a function. To determine whether a table is a function or not, look at the x values. No x value can duplicate. In this case, all x values are different.
Hope this helped.
NEED ALL ANSWERS IN STEPS AND PROPER FULL MANNER
1) Convert decimals to percentages a) 0.543 b) 0.0098 c)1. 67
2) Convert percentages to decimals a) 10% b) 0.010%
3) Convert mixed numbers to fractions and decimals a) 2 1/3 c) 5 3/5
4) Convert fraction to mixed numbers a) 11/4 b) 16/7
Answer:
Step-by-step explanation:
To convert into a percent, multiply by 100
1)
a)0.543; = 0.543*100= 54.3%
b) 0.0098; = 0.0098*100=0.98%
c) 1.67; = 1.67*100=167%
To convert percentages into decimals, divide by 100
2)
a) 10%= 10÷100= 0.1
b) 0.010%= 0.010÷100= 0.0001
To convert mixed numbers into decimals, convert mixed numbers into improper fractions and divide
3)
a)2 1/3= 7/3= 2.333 =233.3%
b)5 3/5= 28/5= 5.6 =560%
To convert a fraction into a mixed number, divide the numerator by the denominator
4)
a) 11/4= 2+3/4= 2 3/4
b) 16/7= 2+2/7= 2 2/7
1. Convert decimals to percentages:
a) 0.543 can be converted to percentage by multiplying it by 100. So, 0.543 x 100 = 54.3%
b) 0.0098 can be converted to percentage by multiplying it by 100. So, 0.0098 x 100 = 0.98%
c) 1.67 can be converted to percentage by multiplying it by 100. So, 1.67 x 100 = 167%
2. Convert percentages to decimals:
a) 10% can be converted to a decimal by moving the decimal two places to the left. So, 10% = 0.10
b) 0.010% can be converted to a decimal by moving the decimal four places to the left. So, 0.010% = 0.0001
3. Convert mixed numbers to fractions and decimals:
a) 2 1/3 can be converted to a fraction by finding a common denominator of 3 and writing the whole number as a fraction. So, 2 1/3 = (2 x 3 + 1) / 3 = 7/3
It can also be converted to a decimal by dividing the numerator by the denominator. So, 7/3 = 2.333...
c) 5 3/5 can be converted to a fraction by finding a common denominator of 5 and writing the whole number as a fraction. So, 5 3/5 = (5 x 5 + 3) / 5 = 28/5
It can also be converted to a decimal by dividing the numerator by the denominator. So, 28/5 = 5.6
4. Convert fractions to mixed numbers:
a) 11/4 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 11/4 = 2 3/4
b) 16/7 can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction. So, 16/7 = 2 2/7
A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly-chosen subject. The psychologist found that X had the given probability distribution.
What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?
answer choices
A. 0.1
B. 0.4
C. 0.8
D. 1
E. Cannot be determined
The probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music cannot be determined (E).
Here 'x' denotes the no. of puzzles completed by an individual within 5 minutes. Given that the probability distribution of 'x' as,
[tex]$$\begin{array}{ccccc}x: 1 & 2 & 3 & 4 \\p(x): & 0.2 & 0.4 & 0.3 & 0.1\end{array}$$[/tex]
'D' is the difference in the number of puzzles saved by two randomly selected subjects. Let [tex]X_{1}[/tex] be the number of puzzles solved by first individual and [tex]$X_2$[/tex] be the number of puzzles solved by [tex]$2^{n d}$[/tex] individual.
Then, D=[tex]X_1-X_2$[/tex] where [tex]$X_1$[/tex] and [tex]$X_2$[/tex] are independent and follow the above
[tex]$$\begin{aligned}& \therefore \text { Variance }(D)=V(D)=v\left(x_1-x_2\right) \\& =V\left(x_1\right)+v\left(x_2\right) \\& =2 \times v\left(x_1\right) \quad\left(\because v\left(x_1\right)=v\left(x_2\right)\right. \\& \text { Now, } V\left(x_1\right)=V(x)=E\left(x^2\right)-[E(x)]^2 \\& =0.2+0.8+0.9+0.4 \\& =2.3 \\&\end{aligned}$$[/tex]
[tex]$$\text { and } \begin{aligned}E\left(x^2\right) & =\sum_{R(x)} x^2 P[x=x] \\& =\sum_{x=1}^4 x^2 P[x \cdot x] \\& =\left(1^2 \times 0.2\right)+\left(2^2 \times 0.4\right)+\left(3^2 \times 0.3\right)+\left(4^2 \times 0.1\right) \\& =6.1 \\\Rightarrow V(x) & =k\left(x^2\right)-[k(x)]^2 \\& =6.1-(2.3)^2 \\& =0.81\end{aligned}$$[/tex]
[tex]$\therefore$[/tex] Variance of D,
[tex]$$\begin{aligned}V(D) & =2 \times v\left(x_1\right) \\& =2 \times 0.81=1.62\end{aligned}$$$\therefore$ Standard deviation of $D$ is,$$\sqrt{V(0)}=\sqrt{1.62} \simeq$$[/tex] 1.27.
Therefore, the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music is, 1.27.
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Can someone help me please
Answer:
[tex]r=14\mathring{}[/tex]
Step-by-step explanation:
[tex](5r-5)\mathring{}+(8r+3)\mathring{}=180\mathring{}\\5r-5+8r+3=180\mathring{}\\13r-2=180\mathring{}\\13r=180\mathring{}+2\\13r=182\mathring{}\\r=\frac{182}{13} \\\\r=14\mathring{}[/tex]
y > x - 3 a. Change the inequality into slope- intercept form, and then change it into an equation.
The slope of the inequality y > x - 3 is 1
What is the slope of an inequality?
The slope of a line is the ratio of the amount that y increases as x increases some amount
To change the inequality y > x - 3 into slope,
substract x from both sides of the inequality
y- x > x - 3-x
= y-x>-3
= y<-3+x
From the inequality y<-3+x the co-efficient of x is 1
Hence, The slope of the inequality is 1
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If the length of a rectangular prism is 4x², the width is
6x³, and the volume is 48x^8, what is the height of the
of the rectangular prism?
The height of the rectangular prism is 2x^3
How to determine the height of the prismThe volume of a rectangular prism is given by the product of its length, width, and height.
We know that the volume is 48x^8, so we can write an equation:
48x^8 = (4x^2)(6x^3)(h)
We can simplify the left side:
48x^8 = 24x^5 * h
And divide both sides by 24x^5 to find the height:
h = 48x^8 / 24x^5 = 2x^3
So the height of the rectangular prism is 2x^3
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Solve for x.
Select the correct response:
19.25
6.5
10
14
Check the picture below.
89.0 mL of a liquid is massed in a graduated cylinder. The total mass is 437.2 g. The empty graduated cylinder has a mass of 277.0 g. What is the density of the liquid?
Paul's Pizza sells pizza by the slice for lunch. An employee recorded how many slices of each type of pizza were sold today. pepperoni 44 cheese 15 supreme 29 Considering this data, how many of the first 76 slices sold during lunch tomorrow should you expect to be slices of pepperoni pizza?
Answer:
To find out how many of the first 76 slices sold during lunch tomorrow should be pepperoni pizza, we can use the information provided about the proportion of pepperoni pizza slices sold today. We can use the following formula to calculate the expected proportion:
(number of pepperoni slices / total number of slices) * 100
Plugging in the numbers we have:
(44 / (44 + 15 + 29)) * 100 = 44 / 88 * 100 = 50%.
So we can expect 50% of the first 76 slices sold during lunch tomorrow to be pepperoni pizza slices, which is equivalent to:
76 slices * 50% = 38 slices
Therefore, we expect 38 of the first 76 slices sold during lunch tomorrow should be slices of pepperoni pizza.
Step-by-step explanation:
A company wants to estimate the mean time it will take workers to complete a certain task. They record the times to complete the task for a random sample of 30 workers. Match the following: ____ mean time to complete a certain task for 30 workers from this company ____ all workers from this company ____ a worker from this company ____ mean time to complete a certain task for all workers from this company ____ 30 workers from this company
____ time to complete a certain task
a. sample
b. parameter
c. individual
d. variable
e. statistic
f. population
1. Mean time to complete a specific task for 30 workers from this company refers to A: sample.
2. All employees from this company are known as F: population
3. A employee from this company is called an C: individual
4. Mean time to complete a specific task for all workers from this company is said to be as B: parameter.
5. 30 employees from this company make E: statistic
6. Time to complete a specific task is called a D: variable
Brief Explaination of each Answer is Given Below:
"Sample" refers to a subset of a larger population that is selected for study. In this case, the "sample" is the 30 workers from the company whose times to complete the task have been recorded.
"Population" refers to the entire set of units or items under study. In this case, the "population" is all workers from the company.
"Individual" refers to a single unit or item in a set. In this case, an "individual" is a single worker from the company.
"Parameter" refers to a characteristic or value that describes a population. In this case, the "parameter" is the mean time it will take all workers from the company to complete the task.
"Statistic" refers to a value that describes a sample. In this case, the "mean time to complete a certain task for 30 workers from this company" is a statistic.
"Variable" refers to a value that can change within a set. In this case, "time to complete a certain task" is the variable of interest.
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Matrix Representation of Linear Regression Recall the linear regression problem from previous statistics class: Suppose that we observe 3 observations (Yi, x),(½, x2),(⅓,Xs) and they take values (0.3,1), (0.8,2), (-0.3,0.1).
The matrix representation of the problem can be written as: ε = [ε1 ε2 ε3]'
The matrix representation of the linear regression problem can be expressed as Y = Xβ + ε, where Y is the n x 1 vector of the dependent variable (Yi),
X is the n x k matrix of the independent variables (xi),
β is the k x 1 vector of coefficients, and
ε is the n x 1 vector of errors.
In this case, n = 3 (number of observations), k = 2 (number of independent variables) and the matrix representation of the problem can be written as:
Y = Xβ + ε
Y = [0.3 0.8 -0.3]
X = [1 1 1; 1 2 0.1]
β = [β0 β1]'
ε = [ε1 ε2 ε3]'
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Three times the sum of a number and 3 is the same as 1 subtracted from the number. Find the number.
Answer:
-5
Step-by-step explanation:
Let x be the number we are trying to find.
According to the problem statement, we know that:
3(x + 3) = x - 1
Expanding and solving for x, we get:
3x + 9 = x - 1
2x = -10
x = -5
So the number we were trying to find is -5.
Please help me with this question.
The volume and radius of the ice cream and the ice cream cone are;
(a) Volume of the ice cream is about 6.3 cubic inches
(b) Radius of needed for the cone to contain 14.5 cubic inches per serving is about 1.422 inches
What is the volume of a solid?The volume of a solid is the space the solid occupies, which is the amount of cube units that fills the solid.
Rotation of a quarter circle to form an hemisphere, by integration is presented as follows;
[tex]\int\limits^1_0 \pi \times ({\sqrt{1-x^2} })^2 \, dx = \frac{2}{3} \cdot \pi[/tex]
The volume of the cone carrying the hemisphere = (1/3)×π×1²×4 = (4/3)·π
The volume of the ice cream = The volume of the cone + The volume of the hemisphere
Therefore;
Volume of the ice cream = (2/3)·π + (4/3)·π = (6/3)·π = 2·π ≈ 6.3
The volume of the ice cream ≈ 6.3 cubic inches(b) Volume of ice cream contained in the new ice cream cone, V = 14.5 cubic inches
The formula for the volume of the ice cream, V = (2/3)·π·r³ + (4/3)·π·r²
Therefore;
V = (2/3)·π·r³ + (4/3)·π·r² (substitution property)
V = (2/3)·π·r³ + (4/3)·π·r²
14.5 = (2/3)·π·r³ + (4/3)·π·r²
(2/3)·π·r³ + (4/3)·π·r² - 14.5 = 0
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Question 1 Use PORS to find m
The measure of ∠R of the given parallelogram is 52°.
What is a parallelogram?
A parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of a similar measure.
Some of the properties of a parallelogram are,
A pair of parallel and opposite sides are equal in lengthThe opposite angles are equal in measureThe sum of adjacent angles is 180°Given,
Length of PS = 3
Length of RS = 5
∠Q = 128°
Since it is a parallelogram,
PS = QR = 3 and RS = QP = 5
∠Q + ∠R = 180
m∠R = 180 - ∠Q = 180-128 = 52°
Therefore the measure of ∠R of the given parallelogram is 52°.
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This question is a challenge question.
The normal price of fuel is 101.6p per litre . Jill has a voucher for 2p off each litre of fuel. She buys 35 liters of fuel and also selects bag of chocolate eclairs at the checkout.
if the eclair cost $1.49 how much does she pay in total?
Ben come aproximadamente 2400 calorías al día. Su esposa Sarah come 5 tanto. Cúantos
¿Sarah come calorías al día?
Sarah consumes 12000 calories per day.
What is calorie?A calorie is a unit of energy.
Given is that Ben eats approximately 2,400 calories a day.
We can write the amount of calories eaten by Sarah as -
y = 5 x 2400
y = 12000
Therefore, Sarah consumes 12000 calories per day.
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{Question in english -
Ben eats approximately 2,400 calories a day. His wife Sarah eats 5 as much. How many calories does Sarah eat a day?}
Isaac is 12
3
4
years old. Sheila is 1
3
8
years younger than Isaac and Jane is 1
1
5
years younger than Sheila. How old is Jane?
Answer:
Step-by-step explanation: 2 00
22
The table below represents a geometric sequence. Determine the recursive function that defines the sequence.
Answer:
C
Step-by-step explanation:
How do we get from 4 to 20? Multiply 4 * 5 = 20.
How do we get from 20 to 100? Multiply 20 * 100.
Thus the answer is C where you multiply 5 by the previous function output.
I saw this pattern from experience, however you could also solve another way:
Simply plug in to the given functions in each answer choice.
For example, A:
f(1) = 4
f(n) = 16 * f(n - 1), for n >= 2
Now test values of n and check if they match the table.
f(1) = 4. This matches the table
f(2) = 16 * f(2 - 1) = 16 * f(1) = 16 * 4 = 64. This does not match the table.
You continue this process with the rest of the answer choices until you find a function, f(n), that gives the correct output of the table.
Greg borrowed money from a credit union for 4 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $1400. How much money did he borrow?
Answer:
Greg borrowed $20,000.
Step-by-step explanation:
To calculate the principal (the amount borrowed), we can use the formula for simple interest:
I = Prt
where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.
Given that:
I = 1400
r = 7% (expressed as 0.07)
t = 4
P = I / (r * t) = 1400 / (0.07 * 4) = $20,000
Therefore, Greg borrowed $20,000.
Select all the equations that match the tape diagram. Tape diagram, 1 part labeled 8, 6 parts labeled x, total 35. A: 35=8+x+x+x+x+x+x+ B: 35=8+6x C: 6+8x=35 D: 6+8=35 E: 6x+8x=35x F: 35-8=6x
The equations that match the tape diagram.
Thus, the correct equations are: A, B, D and F
What is tape diagram?A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams. to use whole numbers, fractions, and ratios to answer problems that include the four operations. Students can improve their problem-solving abilities and algebraic reasoning with the use of tape diagrams.
A visual tool known as a tape diagram represents the components of a ratio using equal-sized boxes. The reason it is named a tape diagram is because it resembles the lengthy strips of sticky tape used to bind documents or wrap gifts.
Thus, from the above given data it is clear that, x = 4.5
Correct option: A, B, D, and F
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at the soccer game last weekend Dave bought three slices of pizza and two bottles of water for $12.75 at the same concession stand Angie bought one slice of pizza and three bottles of water for 7.75. what is the price of each item at the concession stand
Let's start by converting this word problem into math equations... This will make it much easier to choose an approach to the problem!
Write equations for both Dave and Angie. We will use the variables P for slices of pizza, and W for bottles of water bought.
(1) Dave: [tex]3P+2B=12.75[/tex]
(2) Angie: [tex]1P+3B=7.75[/tex]
Now that we have these equations, it's much easier to tell that this is a system of two equations (two equations, two unknowns). To solve this system, we can use a variety of different methods. For this problem, let's use the Elimination method (removing one variable from the equation.
Start by multiplying (scaling) Angie's equation by a factor of -3, so that we will be able to remove Pizza slices from the equation:
(3) [tex]-3(1P+3B=7.75) \equiv -3P-9B=-23.25[/tex]
Now, let's add Angie's new equation to Dave's original:
[tex]-7B=-10.5[/tex]
Notice that we now only have one variable in this simple equation. This is very easy to solve!
Simplify:
[tex]B=1.5[/tex]
Now that we have the price for a bottle of water, we can substitute this value into either (1) Dave's or (2) Angie's original equation to find the price for a slice of Pizza (P). I will substitute into (1) Dave's equation:
Substitute:
[tex]3P+2(1.5)=12.75[/tex]
Simplify:
[tex]3P=9.75[/tex]
Divide:
[tex]P=3.25[/tex]
Finally, we have reached our conclusion... A slice of Pizza costs $3.25 and a bottle of water costs $1.5 at the concession stand! Let me know if you have any questions or want to learn other ways of solving this problem!
Adliyn mows 2 lawns first is 6 meters long and the second is 4 meters wide. The area of the second lawn is 6 times as big but has the same width of the first. What is the length of the second lawn
Answer:
The area of the first lawn is 64 = 24 square meters.
The area of the second lawn is 6 times bigger, so it is 246 = 144 square meters.
As the second lawn has the same width as the first one, 4 meters, we can calculate the length of the second lawn by dividing the area of the second lawn by its width.
So, the length of the second lawn is 144/4 = 36 meters.
